Traditional interferometry is a well-known and potentially highly precise technique that uses the optical phase of a laser with stable optical frequency to measure physical displacement of a surface. (Hariharan, P. (2007). Basics of Interferometry. Elsevier Inc. ISBN 0-12-373589-0.) However, traditional interferometers struggle to achieve absolute distance measurements due to the well-known “fringe ambiguity” problem where the phase value used for detecting distance repeats every integer number of wavelengths of distance. One must therefore know this integer to measure absolute distance, which can be very challenging for optical wavelengths and macroscopic distances. As a result, traditional interferometers typically measure displacement of a surface rather than absolute distance to a surface or separation between multiple surfaces. To create a larger unambiguous measurement region, multiple lasers with stable optical frequencies can be used to synthesize a longer effective wavelength than that of either of the two constituent lasers. This so-called synthetic wavelength interferometry (SWI) has the benefit that determining the integer number of (larger) synthetic wavelengths, and therefore the absolute distance, is easier from a practical standpoint.
Another major drawback of traditional interferometry is that reflections from multiple surfaces can cause measurement errors. This occurs because traditional interferometers measure the combined field phase from all surfaces. Therefore all surfaces in the measurement path have the potential to influence the measured phase and corrupt the measurement.
In contrast to interferometry, various techniques for measuring absolute distances (not just displacement) to surfaces or separations between surfaces by optical means are also known. These techniques include laser triangulation, conoscopic holography, chromatic confocal sensing, frequency-modulated continuous-wave (FMCW) laser radar, swept-frequency optical coherence tomography, and phase modulation range finding. Examples of this can be found in: F. Blateyron, Chromatic Confocal Microscopy, in Optical Measurement of Surface Topography, (Springer Berlin Heidelberg) pp 71-106 (2011), C. Olsovsky, et al., “Chromatic confocal microscopy for multi-depth imaging of epithelial tissue,” Biomed Opt Express. May 1, 2013; 4(5): 732-740, G. Y. Sirat et al., “Conoscopic holography,” Opt. Lett. 10, (1985), W. C. Stone, et al., “Performance Analysis of Next-Generation LADAR for Manufacturing, Construction, and Mobility,” NISTIR 7117, May 2004, and M. A. Choma, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Exp. 11 (18), 2183 (2003). These techniques offer varying levels and combinations of measurement ranges, precisions, and resolutions. However, none of these techniques can match the precision of the best traditional interferometry. Fundamentally, this is because the achievable range resolution of absolute distance measurement techniques (that do not exhibit fringe ambiguity) is limited by the information bandwidth (B) through the relation.ΔRabs=c/2B,  (1)
where c is the speed of light and it has been assumed the measurements are made in vacuum. The analogous interferometric techniques (that do exhibit fringe ambiguity) are limited instead by (half of) the measurement wavelength (including synthetic wavelength) through the relation:ΔRint=λ/2=c/2v  (2)
where v is the optical frequency. In both cases, the achievable measurement precision (or repeatability), defined as the standard deviation of measurements made under identical conditions, is given approximately by the Cramer Rao lower bound, (Cramér, Harald, “Mathematical Methods of Statistics,” (Princeton University Press), ISBN 0-691-08004-6), 1946; Rao, Calyampudi, “Information and the accuracy attainable in the estimation of statistical parameters,” Bull. Calcutta Math. Soc, 37, pp 81-89, 1945),σ≈ΔR/√{square root over (SNR)}  (3)
where SNR is the electrical power signal-to-noise ratio. Quite simply, because v can be made larger than B in practice, the precision of an interferometer can be made better than an absolute distance measurement technique with the same SNR.
Important prior art has worked to combine interferometry with absolute distance measurement techniques to achieve interferometric performance without fringe ambiguity. In U.S. Pat. No. 5,371,587 issued to de Groot et al., which is incorporated herein by reference in its entirety, the authors combined synthetic wavelength interferometry with chirped FMCW laser radar, so-called chirped SWI, and achieved 3 μm root-mean-square standard deviation measurements of distance. As disclosed in U.S. Pat. No. 7,215,413, Soreide et al. demonstrate improvements to the work of de Groot by reducing the complexity of the optical system involved and by incorporating a plurality of reference interferometers and processing to account for the nonlinearities in the optical frequency chirp. As disclosed in U.S. Pat. No. 7,292,347, Tobiason, et al. disclose using quadrature detection, which also simplifies the work of de Groot. In U.S. Pat. No. 9,030,670, Warden et al., disclose a different processing method from Soreide et al. to calculate the distance. More recently, in U.S. Patent Application 2015/0019160 A1, Thurner, et al. disclose adding modulation and demodulation as a method of wavelength multiplexing and demultiplexing, stabilizing the lasers to gas absorption lines, and processing techniques for coping with the nonlinearities in the optical phase.
While some of the different realizations of chirped SWI have produced desirable results, all of the prior art suffers from significant drawbacks. First, the resolution, precision, and accuracy of the results are either limited by nonlinearities in the laser frequency chirp, or complex components and processing must be used to mitigate the frequency chirp nonlinearities. Second, prior art uses either reference interferometers or lasers stabilized to molecular gas absorption lines as length references. However, physical interferometers are susceptible to environmental and mechanical perturbations and are not inherently linked to fundamental atomic or molecular absorption lines. Moreover, stabilization to an absorption line adds complexity and can limit the speed and bandwidth of the laser chirp. Third, the prior art does not teach how to solve the problem of measurement errors due to multiple surface reflections or sub-resolved surface reflections. And finally, none of the prior art teaches how to account for the optical phase shift that can occur upon certain reflections (e.g. from low to high index materials) to enable an accurate absolute distance measurements.
The invention described herein teaches how the prior art may be significantly improved by utilizing highly linearized frequency modulated lasers such as, but not limited to, that disclosed in recently disclosed in Peter A. Roos, Randy R. Reibel, Trenton Berg, Brant Kaylor, Zeb W. Barber, and Wm. Randall Babbitt, “Ultrabroadband optical chirp linearization for precision metrology applications,” Opt. Lett. 34, 3692-3694 (2009), how sweeping over, rather than stabilizing to, spectroscopic absorption lines can be used to directly and fully calibrate length, and how multiple surfaces can be measured simultaneously without traditional interferometric errors, even if they are sub-resolved. The preferred embodiment of this invention enables absolute distance measurements with interferometric precision and accuracy limited by a fundamental NIST-traceable spectroscopic gas absorption frequency.